Chester Higgins Jr. / The New York Times. A co-op in Manhattan with a roof garden.

All are green in one sense. In different ways, each helps to solve serious environmental problems. One issue is air pollution, which needs no introduction. The second is the urban heat island. Because cities have lots of dark surfaces that absorb heat and relatively little green cover, they tend to be hotter than surrounding areas — the average summer temperature in New York City is more than 7 degrees hotter than in the Westchester suburbs. This leads to heavy air-conditioning use — not good — and makes city dwellers miserable. For a few people every year, the heat is more than a discomfort — it’s fatal.

The other problem is storm water runoff. In New York, as in about a fifth of American cities, there is only one sewer system to conduct both rainwater and wastewater. About every other rainfall in New York, sewers flood and back up, discharging their mix of rainwater and wastewater into the city’s waterways. It doesn’t take much to overload New York’s sewers — it can take only 20 minutes of rainfall to start water from toilets flowing into Brooklyn’s waterways. The water does more than flood streets. It makes us sick — cases of diarrhea spike when sewers overflow. When sewers back up, polluted water runs into our lakes and oceans, closing beaches.

How can a new roof help?

At 1:45 in the afternoon on August 9, 2001, the temperature in Chicago was in the 90s. Eleven stories up, on the roof of City Hall, the surface temperature of the black tar measured 169 degrees. But Mayor Daley, environmental innovator, had done something interesting. The year before, a section of the City Hall roof had been painted white. The surface temperature there was between 126 and 130 degrees. And much of the roof of the building had become a garden — 20,000 plants in 150 varieties, chosen for their abilities to thrive without irrigation and stand up to Chicago’s notorious wind. The surface temperature of the green roof varied between 91 and 119 degrees.

So the difference between a black tar roof and a green roof was at minimum 50 degrees. And the green roof was able to retain 75 percent of a one-inch rainfall. The two tasks go hand in hand — green roofs cool by capturing moisture and evaporating it.

Putting living vegetation on the roof is not a new idea. For thousands of years people have made sod roofs to protect and insulate their houses, keeping them cooler in summer and warmer in winter. The modern movement for green roofs began in the last 50 years in Europe. Germany, where about 10 percent of roofs are green, is the leader; some parts of Germany require green roofs on all new buildings.

Greening a roof is not exactly simple though. Over a black roof — flat is easiest but sloped can work — goes insulation, then a waterproof membrane, then a barrier to keep roots from poking holes in the membrane. On top of that there is a drainage layer, such as gravel or clay, then a mat to prevent erosion. Next is a lightweight soil (Chicago City Hall uses a blend of mulch, compost and spongy stuff) and finally, plants.

An extensive roof — less than 6 inches of soil planted with hardy cover such as sedum — can cost $15 per square foot. An intensive roof — essentially a garden, with deeper soil and plants that require watering and weeding — can double that. But because the vegetation is thicker, it will do a better job of cooling a building and collecting rainwater. Plants reduce sewer discharge in two ways. They retain rainfall, and what does run off is delayed until after the waters have peaked.

A study conducted by Columbia University and City University of New York of three test roofs built by Con Edison in Queens found that the green roof — an extensive roof, planted with sedum — cut the rate of heat gained through the roof in summer by 84 percent, and the rate of heat lost through the roof in winter by 34 percent.

Another study (same researchers, same Con Ed test sites) found that green roofs are a very cost-effective way to reduce storm water runoff. If New York has one billion square feet of possibly greenable roof, planting it all could retain 10 to 15 billion gallons of annual rainfall — which would cut a substantial amount of sewage overflow. “If you add in all the other green infrastructure, such as street trees, permeable pavement and ground collection pits, it might be possible to eliminate the combined sewage overflow without building specialized water detention tanks, which are hugely expensive,” said Stuart Gaffin, a research scientist at Columbia’s Center for Climate Systems Research, who co-authored both studies with colleagues from City College.

Green roofs have other advantages. They scrub the air: one square meter can absorb all the emissions from a car being driven 12,000 miles a year, said Amy Norquist, chief executive of Greensulate, which installs green roofs. And green roofs can provide the plants that animals, birds and bees need where parks are far apart.

White roofs are cheap and don’t require any engineering — just a layer of special paint. New York City is trying to coat a million square feet of roof a year. Building owners can do the work themselves, or they can engage CoolRoofs, a city initiative that promotes white roofs and organizes hundreds of volunteer painters. Since 2010, about 3,000 volunteers have coated 288 buildings.

But less investment buys less return. White roofs don’t catch rainwater, help biodiversity or clean the air. Gaffin’s group found that the white portion of the Con Ed roof averaged 43 degrees cooler than black at noon on summer days. That’s something, but it’s a smaller cooling effect than green roofs offer. Green roofs improve each year as vegetation becomes denser and taller. But after a few months, a white roof tends to look like city snow — covered with soot. As a white roof dirties, it loses a lot of its cooling ability.

Another roof option doesn’t save energy — it creates it. New Jersey has installed 500 megawatts of solar power — enough to run half a million homes. California has installed double that. New York City? So far, just 6.5 megawatts.

How have New Jersey and California done it? Private vendors install and maintain the solar panels, and are paid in future energy savings. Scott Stringer, the Manhattan borough president, argues that New York should use this system to put solar panels on the roof of every public school. Stringer’s report says putting solar roofs on all available public schools would eliminate as much carbon emissions as planting 400,000 trees — eight times the number in Manhattan now.

Public schools have become a testing ground for the new roofs. At the Robert Simon complex in the East Village, which houses three schools (my children attend two of those schools), work is beginning this summer on a farm. A committee at the Earth School was looking for green ideas that would go beyond recycling and create a curriculum. Abbe Futterman, the science teacher, was already growing vegetables and fruit in sawed-off pickle barrels right outside her classroom window, using the garden to teach plant science and nutrition. The kids tend it, and use the produce to cook food from around the world.

The Fifth Street Farm will be a much larger vegetable and fruit garden in planters raised above the roof on steel girders — not a classic green roof. The money has come from various government offices — those of Stringer, State Senator Daniel Squadron and City Council member Rosie Mendez. Douglas Fountain, an architect who is assisting the schools in implementing the construction (and a parent of a Tompkins Square Middle School student) said that it was designed to be easily replicable by other schools.

Is a green roof a good investment for a building owner? Perhaps, but the biggest reason might not be reduced energy costs — lots of factors affect a building’s energy use. More savings come from the fact that temperature swings make a black tar roof expand and contract. The smaller the spread, the longer the roof life. Roanoke, Va., for example, just installed a green roof on its municipal building, at a cost of $123,000, adding anywhere from 20 to 60 years to the life of the current roof membrane. “I personally believe a green roof is the last roof you’ll have to put on,” said Gaffin.

But any changes to a black tar roof are undoubtedly good investments for cities — indeed, interest in green roofs is soaring largely because of the sewage problem and the costs of trying to solve it the old way. New York City decided it was more cost effective to build green infrastructure, including green roofs, than to construct more sewer pipes or storage tanks, and it is spending $1.5 billion over the next 20 years on green projects that will reduce rainfall runoff. The goal is to cut sewer outflows by 40 percent by 2030.

“The good news is that this is a ‘no harm’ intervention,” said Carter Strickland, the commissioner of the Department of Environmental Protection. “People want it; there’s a lot of other benefits. If at the end of the day it doesn’t do the full job, whatever you have to build on top will be much smaller and less expensive.”

To encourage building owners to install green roofs, New York City has a pilot program that will end next year offering a $4.50-per-square-foot tax abatement for green roofs that cover more than half a rooftop. (There are also tax abatements for solar-panel roofs.)

New York City was not one of the first American cities to promote green roofs. “But the city is doing quite well,” said Gaffin. “The green infrastructure plan is very ambitious.” The problem is that the little-by-little approach won’t produce real environmental benefits until they reach a critical mass, and that could take a long time. “We get biodiversity benefits from small scale greening, and individual building owners will get an energy benefit,” said Gaffin. “ But to make a difference to the city’s climate or hydrology we’d have to get up to 30, 40 or 50 percent coverage. What we have now is a drop in the bucket.”